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Visual Acuity within the Area Centralis and its Relation to Eye Movements and Fixation
AMERICAN JOURNAL OF OPHTHALMOLOGY Volume 11
December, 1928
Number 12
VISUAL ACUITY W I T H I N T H E AREA CENTRALIS A N D ITS RELATION TO EYE MOVEMENTS A N D FIXATION FRANK W. WEYMOUTH, P H . D . , DON CARLOS H I N E S , A.B., LAWRENCE H. ACRES, A.B., JOHN E. RAAF, A.B., AND MAYNARD C. WHEELER, A.B. STANFORD UNIVERSITY, CALIFORNIA
Using an arrangement of the Ives visual acuity test with other special apparatus which is described, three subjects were studied as to the visual acuity of a central retinal region (in cluding the fovea) with a radius of 85' or 0.42 millimeter from the axis of fixation. A uniform sensory gradient in the light adapted eye was shown to exist, the visual acuity decreasing rapidly but regularly in all directions without breaks or marked variations in rate of change at the margins of any known anatomical areas. The gradient continued to the very center of the retina. The horizontal and vertical meridians showed different rates of decrease of visual acuity. The results support the view that the sensory gradient is the basic factor in eye movements and fixation. From the Department of Physiology, Stanford University.
Our object was to determine the regional visual acuity within and near the area centralis and, if possible, its relationship to the other topographical features of this part of the retina. The general features of the variation of visual acuity with place in the retina have long been known. The early work, such as that of Fick 13 , was followed by the careful determinations of Wertheim in 18942T, which have re mained standard. The latter used grids of various sizes on a p*erimeter at one meter. This method, involving ac commodation and variations in the area stimulated, has obvious limita tions, and, until the advent of more refined technique, detailed acquaint ance with the acuity of the important central region was impossible. Even at the present time, however, search in the literature fails to show any data on the variations of acuity within the area centralis. Marx and Trendelenburg 22 and others have la mented this deficiency. Wertheim's data include the nearest determina tions; namely, at fixation and at 2° 30', but this actually gives only one value for the area centralis, since the second point falls outside at a distance almost
twice that covered by the present in vestigation. Burchardt 6 gives acuities within an excentricity of 1°, but as these were made with test cards of dots of indeterminate angular size and separation on an ordinary perimeter they are of little value. Aubert 1 tested the perception of motion at excentricities including 15' and 1° 15'. In the pages that follow we give our method in some detail, since the accuracy of these determinations rests so largely on the technique employed. Apparatus and conditions: The right eye of each of three subjects, W., Wh., and R., was tested with the Ives visual acuity object. This instrument exhibits through a circular aperture of six cm. diameter a field of alternate black and white lines. These lines are interference bands formed by two grat ings illuminated from behind. By ro tating the gratings one on the other the angle formed by the two rulings may be altered and therefore the width of the interference bands. By rotating the frame carrying the gratings, the direction of the lines may be changed. Alterations in the width of the lines do not change the total amount of light transmitted; therefore the average
947
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FRANK W. WEYMOUTH AND OTHERS
brightness of the test field remains constant. This method of producing lines of variable width has been utilized by Johnson 20 and by Miles 4 . The latter states that it was first described by Behn 3 . The form of the instrument used by us is that devised by Ives 16 ' 17,18 and manufactured by the Bausch and Lomb Optical Company. It is pro vided with scales giving directly the visual acuity at six meters and at submultiples of this distance. It has long been customary in oph thalmology to use for visual acuity a scale based on the standard adopted by Snellen in which a visual angle of one minute for each line or space is con sidered normal. The acuity is then taken as the reciprocal of the visual angle threshold expressed in minutes. We have used this method in the present paper because it is customary, but have also given the actual visual angle thresholds for comparison. It seems clear, however, that this method of expressing acuity is incorrect. As pointed out by Sterling and his coworkers 25 , Snellen used the familiar fractions (20/20, 20/40, and so on) as descriptive of the conditions of the test and not as a measure of the acuity, and for this reason objected to the use of the decimals derived from them. Sterl ing devised "meshed glasses" which reduced the acuity by known amounts, and from the effect of these worn in combination he concluded that the relation-between the visual angle and the true acuity was an exponential one: this corresponds to the logarithmic scale of acuity used in figure 1, which was independently adopted for an en tirely different reason. The instrument was calibrated di rectly, the distance from the center of one line to the center of the next being measured with calipers. Since by definition the visual acuity is the re ciprocal of the separation of the lines, the product of the scale readings and the corresponding measurements of the lines should be constant. This proved not to be true, but on reduction of each scale reading by 0.02 a constant
was obtained. This assumes that the error lay in the position of the entire scale on the instrument. In our de terminations the readings were made on the six-meter scale reduced to twenty-one meters (the distance at which used) and corrected for the above error so that they represent the true reciprocals of the thresholds in minutes. The intervals at which the test object was set were one-thirtieth (one-third of the interval between the tenth marks) on the six-meter scale, corresponding to an interval in visual acuity at twenty-one meters of about 0.1. These were found to be as small intervals as could be set with any de gree of accuracy on the scale. The test object was installed in a small room at the end of a corridor, and at a convenient distance (1.61 m.) from the door. In the door was cut a round hole of six cm. diameter through which the lines were exposed. This door was faced with light grey strawboard of a slight yellow cast. The screen thus formed served the same purpose as that used by Miles to eliminate clues given to the direction of the lines by the oblique meeting of the lines and the circular opening of the instrument in which they are framed. At the distance used no trace of the tell-tale "steps" could be noted. The walls of the corridor were white washed, and th£ illumination was en tirely artificial, coming from a series of 200-watt gas-filled bulbs so shaded that none of the direct light fell on the subject who sat in the corridor facing the test object. A headrest maintained his eye at exactly twenty-one meters from the test object. Only the right eye was used in judg ing. A screen of white cardboard ad justed to the general illumination was placed about twelve inches in front of the left eye in such a position as to conceal the test object from that eye but not from the right. While assur ing monocular judgment of the ob ject, such an arrangement prevented any tendency for dark adaptation. The eyes were tested, particularly for astig-
VISUAL ACUITY matism, and correcting glasses were used where necessary. Between screen and test object was installed a pendulum faced with the same material as the screen. The velocity of the pendulum was ascer tained by attaching to it a smoked paper and allowing it to swing past a tuning fork to which a stylus was at- • tached. A gap was cut in the pendulum sufficiently wide to allow exposure of the test object for 0.1 second as the pendulum swung. The illumination of the pendulum was from the side, so that when it swung the grating of the test object received no light from in front. The brightness of the pendulum was ad justed until at the distance of twentyone meters the part of the pendulum exposed through the orifice in the screen was practically indistinguish able from the screen itself. Thus the screen presented as nearly as possible a uniform field for the subject's eye. The test object was constant in posi tion, while the fixation point, consisting of a black button of about one centi meter diameter, was varied along two meridians—horizontal and vertical—in tersecting at the center of the test ob ject. This caused images of the test object to fall along the horizontal and vertical meridians of the retina having as their pole the axis of fixation. The fixation points were at intervals of six centimeters, starting from the center of the orifice in the screen. As the diameter of this orifice was six centimeters, the circular images made on the retina by the test object at con secutive points of fixation were tan gent. Factors in visual acuity: Among the factors affecting monocular visual acuity, may be included the following 28, 9. 10 .
A.
Factors concerning the eye: 1. Sensibility of retina, varying with a. Age and sex. b. Retinal adaptation 13 . c. Topography of retina 27 . 2. Refractive condition of the eye, varying with
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a. Age and sex. b. Refractive errors. 3. Pupillary diameter. 4. Eye movements 2 . B. Factors concerning the stimu lus 9- 10. 1. Size of test object. 2. Type of test object. 3. Brightness of general illu mination 21 . 4. Contrast between object and background. 5. Time of exposure of object. 6. Wave length of light used. For a particular portion of the retina of an individual eye, discrimination would depend, therefore, on the six external factors, four of which have recently been emphasized by Cobb 10 . In the present work, where regional variations of sensitivity were under in vestigation, all external factors except size of detail of test object were kept constant; the same instrument was used throughout; controlled artificial light was used, giving constant general illumination and consequently constant pupillary size and state of adaptation; the contrast was constant for the in strument ; the time of exposure was kept constant at 0.1 second; and the source of illumination, and therefore the wave length, was unchanged throughout. The brightness of the screen and walls was 14 to 15 millilamberts; that of the test object was 17.9 ml. Since an illumination of ten to fifteen footcandles is considered adequate for even such exacting work as drafting 7 , and since white paper reflects about eighty per cent of incident light, the highest brightnesses encountered under excep tional artificial illumination would not exceed 8 to 13 ml., which is definitely less than the present level. Interior daylight may, however, exceed the in tensity used, since it is stated to range from 4 to 32 ml. The general illumination of the corridor was actually but little different from that to which the subject had previously been exposed; nevertheless a preliminary exposure of five minutes
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FRANK W. WEYMOUTH AND OTHERS
for adaptation to the observing condi 2° 50', or 0.84 mm., in diameter. Pre tions was allowed as a precaution. vious determination on W . gave the The limitation of the exposure to following data: rod-free area, hori 0.1 second precluded eye movements 11 zontal diameter 0.789 mm., vertical which would have had two disturbing diameter, 0.740 mm.; pigmented area, effects: (1) a change in fixation and 0.66 mm. (average) ; nonvascular area, consequently in the location of the horizontal diameter 0.52 mm., vertical image on the area centralis; and (2) an diameter 0.535 mm. Whether the increase in acuity due to movement of • general field tested is concentric with the image 2 . any or all of those mentioned above Experimental procedure: The lines can not, of course, be determined. of the test object were exposed in four The total number of judgments different directions: horizontal, verti given for each area was approximately cal, and right and left oblique. sixty, and the total number for each With a given fixation point, the test eye two thousand. object was set with the lines a given In arriving at the acuity for each distance apart and in a given axis, and area tested, the judgments were scored the pendulum was swung. The sub as follows: each correct "certain" was ject gave his judgment as to the direc counted as two points, each correct tion of the lines, classing it as "certain" "uncertain" as one point, and each "un or "uncertain", or as "unknown". The known" or incorrect judgment as 0. separations and directions of the lines This seemed as simple a method as was were changed in irregular order; but practicable. It is open to the criticism equal numbers at each separation and that if correct guesses count, incorrect direction were given. guesses should discount. As the in After a little experience the critical correct guesses were very few in num range of settings with a given fixation ber and the incorrect certains still point could be forecast rather closely. fewer, their omission did not appre In this range five judgments were ciably affect the result. On this basis recorded for each of the four positions then a score of five in five trials was of the test object at each of the scale considered the fifty per cent mark, or settings used. On an average, three the threshold acuity. This median and settings of the scale included the its probable error were determined by critical range, four out of five correct customary methods. "certains" and four out of five "un For calculation of the size of retinal knowns" being considered satisfactory images and visual angles, the following limits. method was used 26 : An inherent source of variability is Let the difficulty of maintaining accurate x = distance of object from first fixation, particularly with small de focal point, grees of excentricity. Fatigue was y = size of object found to be such an important factor y' = size of retinal image that only short periods of observation wf = angle in radians subtended were employed, with ample rest be by object at first nodal tween. The best proof of the care point and by image at taken on these points is that the varia second nodal point, tions, and consequently the probable and errors, of the results are as small as F = refractive power of eye they are. For each eye the acuity was deter (58.64 D. for Gullstrand's schematic eye). mined for thirty-three retinal areas: for that surrounding the axis of fixa Then tion and for eight tangent areas on i y each side in the horizontal and vertical X X meridians. This covers a field about
951
VISUAL ACUITY and
■('4) approximately
xF In this case, for the test object x = 21 m., while for the screen x = 19.39 m. On this basis the subject's visual angle for the test object and also for the interval between successive fixation points was 10.64', which corresponds to a retinal distance of 0.05277 mm.
The size of retinal image correspond ing to a visual angle of 1' is 4.96 microns. The maximum average axial acuity (determined by fixing the test object) was found to be 1.54 (in the case of W . ) , in which case the distance from the center of the image of a black line to that of the adjacent white line would be 3.22 microns. It is interest ing to compare this figure with that of Fritsch 14 , who gives the average interconal distance as about 3 microns! Results and discussion: Although a greater number of observations would undoubtedly give a more completely representative curve of acuity, the
TABLE 1
Visual acuity and threshold for each part of visual field tested (W). Average for all directions
Direction of lines of test obj ect Excentricity Direct fixation 0' Nasal meridian 10.64' 21.27' 31.91' 42.54' ' 53.18' 63.82' 74.46' 85.08' Temporal meridian 10.64' 21.27' 31.91' 42.54' 53.18' 63.82' 74.46' 85.08' Inferior meridian 10.64' 21.27' 31.91' 42.54' 53.18' 63.82' 74.46' 85.08' Superior meridian 10.64' 21.27' 31.91' 42.54' 53.18' 63.82' 74.46' 85.08'
right oblique acuity
left oblique acuity
vertical acuity
1.53
1.44
1.63
1.56
1.60 1.38 1.28 1.12 1.08 1.01 0.92 0.92
1.30 1.08 1.14 1.05 1.03 0.98 0.92 0.91
1.67 1.38 1.30 1.17 1.17 1.05 0.94 0.92
1.54 1.53 1.42 1.26 1.24 1.17 1.17 1.05
1.40 1.28 1.30 1.17 1.24 0.99 0.99 0.94
1.49 1.35 1.30 1.23 1.21 0.96 0.94 0.99
1.65 1.38 1.42 1.30 1.24 1.07 1.01 0.98
1.37 1.30 1.03 0.89 0.82 0.76 0.71 0.59
1.28 1.08 1.08 0.78 0.82 0.73 0.69 0.64
1.38 1.33 1.05 0.94 0.83 0.83 0.69 0.67
1.47 1.26 1.24 0.97 0.91 0.94 0.75 0.73
horizontal acuity
acuity P.E.
threshold seconds
1.54 ±0.0057
39.0
1.53+0.0063 1.34+0.0101 1.29+0.0073 1.15+0.0050 1.13+0.0057 1.05+0.0050 0.99+0.0066 0.95+0.0049
39.2 44.8 46.5 52.2 53.1 57.1 60.6 63.2
1.49 1.50 1.51 1.37 1.35 1.26 1.19 1.10
1.51 1.38 1.38 1.27 1.26 1.07 1.03 1.00
39.7 43.5 43.5 47.2 47.6 56.1 58.3 60.0
1.56 1.38 1.17 0.99 1.05 0.92 0.75 0.70
1.53 1.19 1.15 0.96 0.87 0.78 0.71 0.70
1.44 1.24 1.11 0.91 0.89 0.80 0.72 0.66
41.7 48.4 54.1 65.9 67.4 75.0 83.3 90.9
1.53 1.53 1.30 1.12 0.96 0.96 0.91 0.73
1.44 1.31 1.28 1.08 0.96 0.94 0.85 0.78
1.46 1.36 1.22 1.03 0.92 0.92 0.80 0.73
41.2 44.1 49.2 58.3 65.2 65.2 75.0 82.2
•
952
FRANK W. WEYMOUTH AND OTHERS TABLE 2
Table giving for all three subjects the average visual acuity and threshold at each distance from the axis of fixation. Excentricity of center of area tested angular distance minutes 0 10.64 21.27 31.91 42.54 53.18 63.82 74.46 85.08
retinal distance mm. 0 0.0528 0.1055 0.1583 0.2111 0.2639 0.3166 0.3694 0.4222
Average of all meridians Wh
W
R
acuity
seconds
acuity
seconds
acuity
seconds
1.54 1.49 1.33 1.25 1.09 1.05 0.96 0.89 0.83
39.0 40.3 45.1 48.0 55.5 57.2 62.5 67.5 72.3
1.45
41.4
0.98
61.2
1.19 1.12 1.02 0.94 0.81 0.78 0.66
50.4 53.6 58.8 63.8 74.1 76.9 90.9
0.77 0.82 0.72 0.73 0.67 0.54 0.51
77.9 73.2 83.3 82.2 89.6 111.1 117.7
present data, which are more extensive and accurate than those previously available, seem to show conclusively several important features. First : The area centralis shows a
uniform sensory gradient essentially similar to that for the entire retina as determined by Wertheim 27 . This is clearly shown in figure 1, and by cornparison of figures 5 and 6.
ANGULAR DISTANCE BETW££N F/XATIOU POINT AND IM/K£
Fig. 1. (Weymouth). Comparison of Wertheim's data on central visual acuity (circles) with those of W. in the present work (points). The boundaries of the nonvascular, pigmented, and rod-free areas of W. are indicated. The ordinates represent the logarithms of the visual acuities scaled to a fixation value of unity for comparison.
VISUAL ACUITY
The peripheral decline of acuity is without apparent breaks or changes, but forms a continuous gradient on which the anatomical margins of the fovea or other central areas are not indicated. In other words, the margins of the rod-free area, of the pigmented area (macula), and of the nonvascular area are not reflected in the acuity, whatever other physiological relations may be shown for them. W e must conclude that, as far as acuity is con cerned, foveal and extrafoveal photopic or light-adapted vision are basically the same. The angular limits of "central acuity" can be set only arbitrarily. Second: The gradient is a continu ous one from a sharp maximum at the axis of fixation (presumably the center of the fovea); and points separated radially by as little as 10.64' or 0.0528 mm. show distinct differences of acuity. The general averages of the three sub jects are shown in figure 2. It must be recalled that successive points of fixation caused images of the test object to fall on the retina in the
U.64-'
21. ZT
31.9/'
953
form of tangent circles of 52.77 microns diameter along the horizontal and vertical meridians. Each determina tion, although plotted as a point, tests, then, the acuity of a circular area of about 0.002187 sq.mm. or 2187 sq. microns, and containing about 227 cones. Whether the acuity represents in each case the average or the maximum sensitivity of the area cannot, of course, be determined. If it is the average, the results tend to be smoothed, a process which would reduce the sharpness of the central peak. If it is the maximum, as seems more probable, then we are testing in each area the portion nearest the axis of fixation, and the first excentric determination is in reality more nearly at 5' from the axis pf fixation than at 10.64' (corresponding to the center of the area). The net effect in such a case is to necessitate plotting each determination approximately 5' nearer the axis of fixation. The relation between the peripheral points or areas is not seri-
4Z.54-'
53./a'
63.az?
74.46'
AUGL£ FROM Axis OF FIXATION
Fig. 2 (Weymouth). The average acuity of the three subjects scaled to a fixation acuity of unity for comparison.
6&06'
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FRANK W. WEYMOUTH AND OTHERS
ously changed, but the first interval, between fixation and 10.64', is reduced by almost half. As the first peripheral value is plotted at 10.64', the apparent sharpness of the peak in acuity at fixa tion is less than it probably should be. This peak has important bearings on the relation of the sensory gradient to eye movements and fixation, as will be pointed out later.
error of ± 0.0076. Probable errors and their relative magnitude for the nasal meridian of W. are shown on the curve in figure 3. This meridian is entirely characteristic and shows a much natter gradient than either of the two vertical meridians. The most difficult comparison is that of fixation and a point 10.64' excentric.
40"
45-
I
i-60'
/0.64'
2/. 27' -31.91' 4-2.54-' 53.18' ANGLE PROM AXIS OF FIXATIO/V
63.8?
74.46'
85.08'
Fig. 3 (Weymouth). Acuity for the nasal meridian of W.'s visual field with the probable errors of each determination. Successive d e t e r m i n a t i o n s seem in m o s t i n s t a n c e s t o b e significantly different. T h u s p o i n t s a t 53 + ' and 64 + ' on t h e s m o o t h e r of t h e less s h a r p g r a d i e n t s for W . s h o w a difference in visual a c u i t y of 0.08 w i t h a p r o b a b l e
W . w a s t h e only subject w h o felt t h a t h e could satisfactorily m a i n t a i n fixa tion a t t h a t slight excentricity, the a n g u l a r n e a r n e s s of the test object b e i n g too d i s t r a c t i n g for t h e less ex perienced subjects. S u c h a comparison
TABLE 3
Position of test object Nasal Temporal Inferior Superior
Fixation acuity 1.54 1.54 1.S4 1.54
10.64' acuity 1.53 1.51 1.44 1.46
Difference 0.01 0.03 0.10 0.08
P.E. of difference ±0.0084 ±0.0087 ±0.0093 ±0.0089
VISUAL ACUITY
955
r*T
45"
50"
J 70"
-e
21.27'
31.91' ANGLE
-42.54'
FROM
AXIS
53.I&' OF
63.32'
74.46'
<35.0&
FIXATION
Fig. 4 (Weymouth). The acuity of W. in the four meridians of the visual field. SUPERIOR
TEMPORAL
90' ao' 70' 6cr so- *& 30- zo' io-
FROM
IO1
AXIS
zo' 30' -ro' so1 60 ro- ec sor OF
FIXATION
Fig. 5 (Weymouth). Isopteral chart of W. showing points of equal acuity together with the diameters of the nonvascular (N.V.), pigmented (P.), and the rod-free (R.F.) areas,
956
FRANK W. W E Y M O U T H AND O T H E R S
for W., however, shows differences and probable errors as shown in table 3. The first one of these is not sig nificant and the second is on the borderline, but the iast two are definitely significant, and the whole must be considered so, as in no case is the determination at 10.64' greater than at fixation. Even though this first excentric determination was not ob tained for the other subjects, the trend of the gradient would require a similar difference.
retina, but either the average or the maximum of an area. Third: The different meridians used show different rates of change of acuity, as given for W. in figure 4; the horizontal showing in general the higher acuity in all three subjects. These results are more clearly repre sented in the isopteral diagram (figure 5) in which the points of equal acuity on the four chief meridians of the right eye of W. are connected. The observa tions of Wh. present a similar picture. SUPERIOR
TEMPORAL
35°
30° 25° 20° 15° 10° 5° ANGLE
FROM
0° AXIS
5°
10° 15° 20° 25° 30° 35° 4-0°
OF
FIXATION
Fig. 6 (Weymouth). Isopteral chart of entire visual field based on Wertheim's data for the four principal meridians; for comparison with figure 4.
That the difference is even greater than that shown is indicated by a con sideration of two factors: a. Gross inaccuracies of fixation would tend to be toward the test ob ject rather than away, as it is the center of interest. This tends not only to decrease the apparent difference in acuity but also to increase the probable error by spreading the distribution of judgments. b. As discussed above, each de termination tests, not a point on the
An isopteral graph constructed from the data of Wertheim 27 is given for comparison (figure 6). W e obtained the following order of descending acuity: temporal, nasal, superior, inferior. Wertheim's order for the periphery (points excentric 20° or more) is: temporal, nasal, inferior, superior. The visual field, which is actually an isopter (but for light sense rather than for acuity), shows the order: temporal, inferior, nasal, su perior 12 . The fields for colors are
957
VISUAL ACUITY
similar to that for white light. It is to be noted that the inferior meridian, while of least acuity in and near the fovea, shows a relatively lesser rate of fall of acuity than do the other meri dians, which remain in the same rela tion to each other. An unexpected discovery was that of a relation between the visual acuity and the direction of the lines of the test object with reference to the axis of fixation. In each case the acuity was higher when the lines pointed
A, horizontal meridian tested with horizontal lines. B, horizontal meridian tested with vertical lines. C, vertical meridian tested with vertical lines. D, vertical meridian tested with horizontal lines.
The explanation is not perfectly clear. The right eye of the subject whose values are quoted is not astig matic by the ordinary tests. The ex posure was supposedly short enough to preclude fixative eye movements such
ut r3S"
1.6 1.4
\ x
1.0
0
/0.64-'
21.2?'
<3W ANGLE
Fig. 7 (Weymouth). test object for W.
42.54-' FROM AXIS
33.18' OF
63.82'
74.46'
85.08
FIXATION
Relation between the acuity and the direction of the lines of the
toward the axis of fixation than when they were perpendicular to that direc tion. Thus, it was found that in the vertical meridian the acuity was higher for the vertical direction of the lines than for the horizontal, while in the horizontal meridian the acuity was higher for the horizontal than for the vertical lines, the effect being more marked in the latter case. This is shown graphically in figure 7. It will also be noted that with direct fixation vertical lines are better perceived.
as would tend to blur lines which were not parallel to the direction of move ment, but this factor cannot wholly be excluded nor its importance de termined. The explanation may lie in a different configuration of retinal elements in the meridional direction, giving an actual higher acuity when the points distinguished have their separation at right angles to the meridian. Sensory gradient and fixation: The present investigation seems to have its
958
FRANK W. WEYMOUTH AND OTHERS
greatest significance in relation to fixa tion. Those sense organs presenting an extensive sensory field show differ ences of sensitivity in different parts of this field. If such topographical differences are regular and uniform, we may speak of a sensory gradient or gradient of sensitivity. The eye pre sents such a sensory gradient in a more marked degree than any other recep tor ; the present work serves to extend our knowledge of this gradient into the area centralis; and, as we shall show, such a gradient is fundamental for fixa tion and those eye movements which bring it about. In considering the basis of fixation, we must remember that it is a response on the part of the ocular muscles to a stimulus received on the retina, the re sponse being effected through the central nervous system. The accuracy of such a reaction is, of course, depend ent on the least sensitive element in it, just as the strength of a chain is de pendent on its weakest link. And so, if investigation of the relative sensi tivity of the various elements shows some more accurate than the complete act of fixation itself, then we may rule them out as the limiting factors in fix ation, although all the elements are of course necessary to fixation. For our purposes, the reaction of fixation may be divided into the two elements, sensory and motor, the first including the excitation of the retinal receptors and the integration of the nervous impulses so caused into a per ception in the central nervous system, the second including the activation of the ocular muscles. The accuracy of these two inclusive factors has to some extent been measured; that of their subdivisions has not been analyzed. As to the accuracy of the act of fixation itself, the most careful deter mination is that of Marx and Trendelenburg 22 . With graphic methods ac curate to 15 or 20", they observed in maintained fixation oscillating fluctua tions of about 1' on which were super imposed irregular fluctuations of 4 to 5'. These larger movements they in terpret as due to corrective movements
arising when the image departs more than 2.5' from the center of a fixation area. When two points a short dis tance (18' 17") apart were alternately fixed, the errors were not greater than the variations in fixation of a single point. The limit of accuracy of fixa tion as a whole, then, appears to be 2.5'. The limit of accuracy of the motor part is difficult of determination, since it is almost impossible to separate it from some sensory element. One method of approach to the problem would appear to be that of the thresh old for binocular perception of dis tance (parallax and all distinguishing features of object and surroundings be ing eliminated), so that the determin ing factor is the perception of differ ences in convergence. Fulfilling such requirements are the determinations of Bourdon 5 . Using successive ex posures of a stationary object at dif ferent distances, he obtained a thres hold of about 4' at 25m. The deter minations of Wundt 2 9 , which gave a threshold of 1' 24", are open to objec tion on the grounds of method. Such a determination, however, in volves the perception of changes in the relative position of the two bulbs, a perception which is not necessary to fixation, where the accuracy is checked by exteroceptive sensations from the retina rather than by proprioceptive from the motor apparatus of the bulb. The threshold here cited seems more likely that for the perception than for the motion. Chiba 8 , using the records of Marx and Trendelenburg 22 , considers the small oscillations of the eyeball as the smallest muscular movements ( = 1'). He finds the number in a lateral turn of 40° about equal to the number of fibers in the abducens nerve. While capable of other interpretations, such data are at least highly suggestive, and of course the ultimate limit of control would thus be the coming in or falling out of one nerve fiber. This limit may or may not be 1' and also may or may not be under voluntary control. In other words, we have no definite de-
VISUAL ACUITY termination of the accuracy of the motor element. As for the keenness of the sensory part of the reaction, Averill and Weymouth 2 find that the threshold for the perception of displacements in seg ments of a straight line may be as small as 0.04' (0.02 micron on the retina), an angular distance 1/60 that of the accuracy of fixation. The eye can, then, perceive differences sixty times smaller than it can fix separately; so that fineness of fixation cannot be immediately dependent on fineness of perception. To be distinguished from fineness of perception (or visual acuity in the broad sense) is change of fineness of perception (or sensory gradient). The two do not necessarily parallel each other, for a high acuity may be uni form, giving a low gradient, or a low acuity may fall off rapidly, giving a high gradient. We have left to con sider, then, this sensory gradient. The idea that variation of acuity, or sensory gradient, is the basis of fixa tion is not a new one. Javal 19 pro pounded it as long ago as 1896, and Duane 12 (pages 267, 290, 342) reitera ted it in 1924, although realizing the lack of information regarding sensory gradient within the fovea. Marx and Trendelenburg 22 believe their "fixa tion area" is based on differences of acuity within the area centralis, the image being brought back to the area of maximum acuity as soon as it be comes of appreciably less than the maximum distinctness. To the view that a sensory gradient is the basis of fixation strong support is lent by the work of Simon 24 on fixation in scotopic or dark adaptation. H e finds that with the relative depression of central vision in dark adaptation the most sensitive portion of the retina be comes extracentral, and a new axis of fixation as much as 2° from the one used in bright light may be selected. The direction varies with different sub jects, and fixation is less accurate and rapid. Observations of similar new fixation points in strabismus have been recorded, but accurate information is
959
scarce. Simon believes the position of the fixation point in dark adaptation to rest on a balance between falling acuity and rising sensitivity to light as we pass out of the fovea. While the motor element can not at the present time be entirely eliminated as the possible factor determining the accuracy of fixation, the work of Simon seems to show almost conclusively that the point or axis of fixation is deter mined by the sensory gradient, the im age being made to fall on that part of the retina where it is perceived with greatest distinctness. And it seems en tirely logical that if the sensory gradient determines the area on which the image falls when an object is fixed, it must also determine the accuracy with which the image is maintained on that area. In other words, if the sensory gradient determines the axis of fixation it must also determine the accuracy of fixation. That a significant difference in vis ual acuity exists within 2.5' of the axis of fixation is entirely consistent with the present work. While our nearest determination is probably somewhere between 6' and 11', as brought out above, the results are significant enough to admit a threshold as close to the axis of fixation as 2.5'. Further determinations with more refined methods will doubtless estab lish this threshold and more closely approximate the exact gradient and its peak. Summary The present work is an investigation of the visual acuity of a central retinal region (including the fovea) with a radius of 85' or 0.42 mm. from the axis of fixation. The method of observation gives significant results for three obser vers as indicated by the probable er rors. 1. In the light adapted eye a uniform sensory gradient is shown to exist in this central area similar to that found in the entire retina (cf. Wertheim, Aubert, Fick, and others). The visual acuity attains a sharp maximum at the axis of fixation; it decreases rapidly but regularly in all directions; it shows
960
FRANK W. W E Y M O U T H AND O T H E R S
no breaks or marked variations in rate 3. The horizontal and vertical meridof change at the margins of any of the ians (the only ones tested) are shown known anatomical areas (fovea, rod- to have different rates of decrease of free area, pigmented area or macula, visual acuity from the axis of fixation. or nonvascular area). 4> T h e a c u i t y i s s h o w n t o b e h i g h e r 2. A significant difference is shown w n e n the lines of the test object point to exist for two observers between di- toward the axis of fixation. rect fixation and 22' and for one obr^, ,, , , ... c i n, . • ,< . .. , 5. 1 hese results strongly support the server for 11% showing that the grad. ,, , ., A- K ■ »L ient continues to the v i r y center of the ™ w h a t t h e s e n s o r v & r a d ' e n t 1S, * h e retina. A similar retinal gradient is b a s l c f a c t o r l n e v e movements and fixatlon indicated by Wertheim to 2° 30' and by Aubert to 1° 15'. Stanford University. Bibliography 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
Aubert, Hermann. Pfliiger's Arch. f. d. ges. Physiol., 1886, v. 39, pp. 347-370. Averill, H. L., and Weymouth, F. W. Jour. Comp. Psych., 1925, v. 5, pp. 147-176. Behn, U. Ber. d. deutscher physikal. Gesellsch., 1906, v. 4, pp. 205-208. Benedict, F. G., Miles, W. R., Roth, P., and Smith, H. M. Human vitality and effi ciency under prolonged restricted diet. Carnegie Inst. Pub. no. 280, 1919, pp. 169176 and 607-611. Bourdon, B. La perception visuelle d'espace. Paris, 1902, p. 237. Burchardt, M. Internationale Sehproben, 4 ed. Berlin, 1893, p. 11. Cady, Francis E., and Dates, Henry B. Illuminating Engineering. New York, 1925. Chiba, M. Pfliiger's Arch. f. d. ges. Physiol., 1926, v. 212, pp. 150-157. Cobb, Percy W. Jour. Exp. Psychol., 1927, v. 10, pp. 350-364. Cobb, Percy W. Trans. Ilium. Eng. Soc, 1928, v. 23, pp. 496-506. Dodge, Raymond. Psychological Review Monographs, 1907, v. 8, p. 4. Duane, Alexander. Fuchs's Textbook of Ophthalmology, 8th ed. Philadelphia, 1924. Fick, A. Eugen. Arch. f. Ophth., 1898, v. 45, pp. 336-356. Fritsch, Gustav. Uber Bau und Bedeutung der Area centralis des Menschen. Berlin, 1908. Hartridge, H. Jour. Physiol., 1922, v. 57, pp. 52-67. Ives, Herbert E. Electrical World, 1910, v. 40, p. 939. Ives, Herbert E. Abst. Bull. Phys. Lab. Nat. Electr. Lamp Assoc, 1913, v. 1. Ives, Herbert E. Jour. Opt. Soc. Am., 1917, v. 1, pp. 101-107. Javal, Emile. Manuel du Strabisme. Paris, 1896, p. 28. Johnson, H. M. Jour. Animal Behavior, 1914, v. 4, pp. 319-339. Johnson, H. M. Jour. Exp. Psychol., 1924, v. 7, pp. 1-44. Marx, Eugen, and Trendelenburg, Wilhelm. Zeit. f. Psychol. u. Physiol. d. Sinnesorg., sec. 2, 1911, v. 45, pp. 87-102. Miles—see Benedict and Miles. Simon, Richard. Zeit. f. Psychol. u. Physiol. d. Sinnesorg., 1904, sec. 2, v. 36, pp. 186-193. Snell, Albert C, and Sterling, Scott. Arch, of Ophth., 1925, v. 54, pp. 443-461. Southall, James P. C. Mirrors, Prisms, and Lenses. New York, 1923, p. 448. Wertheim, Th. Zeit. f. Psychol. u. Physiol. d. Sinnesorg, 1894, sec. 2, v. 7, pp. 172189. Wood, Casey. Amer. Encycl. of Ophth., 1918, v. 13, p. 10019, and v. 6, p. 4640. Wundt, Wilhelm. Beitrage zur Theorie der Sinneswahrnehmung. Leipzig and Heidel berg, 1862, p. 195.
December, 1928
Number 12
VISUAL ACUITY W I T H I N T H E AREA CENTRALIS A N D ITS RELATION TO EYE MOVEMENTS A N D FIXATION FRANK W. WEYMOUTH, P H . D . , DON CARLOS H I N E S , A.B., LAWRENCE H. ACRES, A.B., JOHN E. RAAF, A.B., AND MAYNARD C. WHEELER, A.B. STANFORD UNIVERSITY, CALIFORNIA
Using an arrangement of the Ives visual acuity test with other special apparatus which is described, three subjects were studied as to the visual acuity of a central retinal region (in cluding the fovea) with a radius of 85' or 0.42 millimeter from the axis of fixation. A uniform sensory gradient in the light adapted eye was shown to exist, the visual acuity decreasing rapidly but regularly in all directions without breaks or marked variations in rate of change at the margins of any known anatomical areas. The gradient continued to the very center of the retina. The horizontal and vertical meridians showed different rates of decrease of visual acuity. The results support the view that the sensory gradient is the basic factor in eye movements and fixation. From the Department of Physiology, Stanford University.
Our object was to determine the regional visual acuity within and near the area centralis and, if possible, its relationship to the other topographical features of this part of the retina. The general features of the variation of visual acuity with place in the retina have long been known. The early work, such as that of Fick 13 , was followed by the careful determinations of Wertheim in 18942T, which have re mained standard. The latter used grids of various sizes on a p*erimeter at one meter. This method, involving ac commodation and variations in the area stimulated, has obvious limita tions, and, until the advent of more refined technique, detailed acquaint ance with the acuity of the important central region was impossible. Even at the present time, however, search in the literature fails to show any data on the variations of acuity within the area centralis. Marx and Trendelenburg 22 and others have la mented this deficiency. Wertheim's data include the nearest determina tions; namely, at fixation and at 2° 30', but this actually gives only one value for the area centralis, since the second point falls outside at a distance almost
twice that covered by the present in vestigation. Burchardt 6 gives acuities within an excentricity of 1°, but as these were made with test cards of dots of indeterminate angular size and separation on an ordinary perimeter they are of little value. Aubert 1 tested the perception of motion at excentricities including 15' and 1° 15'. In the pages that follow we give our method in some detail, since the accuracy of these determinations rests so largely on the technique employed. Apparatus and conditions: The right eye of each of three subjects, W., Wh., and R., was tested with the Ives visual acuity object. This instrument exhibits through a circular aperture of six cm. diameter a field of alternate black and white lines. These lines are interference bands formed by two grat ings illuminated from behind. By ro tating the gratings one on the other the angle formed by the two rulings may be altered and therefore the width of the interference bands. By rotating the frame carrying the gratings, the direction of the lines may be changed. Alterations in the width of the lines do not change the total amount of light transmitted; therefore the average
947
948
FRANK W. WEYMOUTH AND OTHERS
brightness of the test field remains constant. This method of producing lines of variable width has been utilized by Johnson 20 and by Miles 4 . The latter states that it was first described by Behn 3 . The form of the instrument used by us is that devised by Ives 16 ' 17,18 and manufactured by the Bausch and Lomb Optical Company. It is pro vided with scales giving directly the visual acuity at six meters and at submultiples of this distance. It has long been customary in oph thalmology to use for visual acuity a scale based on the standard adopted by Snellen in which a visual angle of one minute for each line or space is con sidered normal. The acuity is then taken as the reciprocal of the visual angle threshold expressed in minutes. We have used this method in the present paper because it is customary, but have also given the actual visual angle thresholds for comparison. It seems clear, however, that this method of expressing acuity is incorrect. As pointed out by Sterling and his coworkers 25 , Snellen used the familiar fractions (20/20, 20/40, and so on) as descriptive of the conditions of the test and not as a measure of the acuity, and for this reason objected to the use of the decimals derived from them. Sterl ing devised "meshed glasses" which reduced the acuity by known amounts, and from the effect of these worn in combination he concluded that the relation-between the visual angle and the true acuity was an exponential one: this corresponds to the logarithmic scale of acuity used in figure 1, which was independently adopted for an en tirely different reason. The instrument was calibrated di rectly, the distance from the center of one line to the center of the next being measured with calipers. Since by definition the visual acuity is the re ciprocal of the separation of the lines, the product of the scale readings and the corresponding measurements of the lines should be constant. This proved not to be true, but on reduction of each scale reading by 0.02 a constant
was obtained. This assumes that the error lay in the position of the entire scale on the instrument. In our de terminations the readings were made on the six-meter scale reduced to twenty-one meters (the distance at which used) and corrected for the above error so that they represent the true reciprocals of the thresholds in minutes. The intervals at which the test object was set were one-thirtieth (one-third of the interval between the tenth marks) on the six-meter scale, corresponding to an interval in visual acuity at twenty-one meters of about 0.1. These were found to be as small intervals as could be set with any de gree of accuracy on the scale. The test object was installed in a small room at the end of a corridor, and at a convenient distance (1.61 m.) from the door. In the door was cut a round hole of six cm. diameter through which the lines were exposed. This door was faced with light grey strawboard of a slight yellow cast. The screen thus formed served the same purpose as that used by Miles to eliminate clues given to the direction of the lines by the oblique meeting of the lines and the circular opening of the instrument in which they are framed. At the distance used no trace of the tell-tale "steps" could be noted. The walls of the corridor were white washed, and th£ illumination was en tirely artificial, coming from a series of 200-watt gas-filled bulbs so shaded that none of the direct light fell on the subject who sat in the corridor facing the test object. A headrest maintained his eye at exactly twenty-one meters from the test object. Only the right eye was used in judg ing. A screen of white cardboard ad justed to the general illumination was placed about twelve inches in front of the left eye in such a position as to conceal the test object from that eye but not from the right. While assur ing monocular judgment of the ob ject, such an arrangement prevented any tendency for dark adaptation. The eyes were tested, particularly for astig-
VISUAL ACUITY matism, and correcting glasses were used where necessary. Between screen and test object was installed a pendulum faced with the same material as the screen. The velocity of the pendulum was ascer tained by attaching to it a smoked paper and allowing it to swing past a tuning fork to which a stylus was at- • tached. A gap was cut in the pendulum sufficiently wide to allow exposure of the test object for 0.1 second as the pendulum swung. The illumination of the pendulum was from the side, so that when it swung the grating of the test object received no light from in front. The brightness of the pendulum was ad justed until at the distance of twentyone meters the part of the pendulum exposed through the orifice in the screen was practically indistinguish able from the screen itself. Thus the screen presented as nearly as possible a uniform field for the subject's eye. The test object was constant in posi tion, while the fixation point, consisting of a black button of about one centi meter diameter, was varied along two meridians—horizontal and vertical—in tersecting at the center of the test ob ject. This caused images of the test object to fall along the horizontal and vertical meridians of the retina having as their pole the axis of fixation. The fixation points were at intervals of six centimeters, starting from the center of the orifice in the screen. As the diameter of this orifice was six centimeters, the circular images made on the retina by the test object at con secutive points of fixation were tan gent. Factors in visual acuity: Among the factors affecting monocular visual acuity, may be included the following 28, 9. 10 .
A.
Factors concerning the eye: 1. Sensibility of retina, varying with a. Age and sex. b. Retinal adaptation 13 . c. Topography of retina 27 . 2. Refractive condition of the eye, varying with
949
a. Age and sex. b. Refractive errors. 3. Pupillary diameter. 4. Eye movements 2 . B. Factors concerning the stimu lus 9- 10. 1. Size of test object. 2. Type of test object. 3. Brightness of general illu mination 21 . 4. Contrast between object and background. 5. Time of exposure of object. 6. Wave length of light used. For a particular portion of the retina of an individual eye, discrimination would depend, therefore, on the six external factors, four of which have recently been emphasized by Cobb 10 . In the present work, where regional variations of sensitivity were under in vestigation, all external factors except size of detail of test object were kept constant; the same instrument was used throughout; controlled artificial light was used, giving constant general illumination and consequently constant pupillary size and state of adaptation; the contrast was constant for the in strument ; the time of exposure was kept constant at 0.1 second; and the source of illumination, and therefore the wave length, was unchanged throughout. The brightness of the screen and walls was 14 to 15 millilamberts; that of the test object was 17.9 ml. Since an illumination of ten to fifteen footcandles is considered adequate for even such exacting work as drafting 7 , and since white paper reflects about eighty per cent of incident light, the highest brightnesses encountered under excep tional artificial illumination would not exceed 8 to 13 ml., which is definitely less than the present level. Interior daylight may, however, exceed the in tensity used, since it is stated to range from 4 to 32 ml. The general illumination of the corridor was actually but little different from that to which the subject had previously been exposed; nevertheless a preliminary exposure of five minutes
950
FRANK W. WEYMOUTH AND OTHERS
for adaptation to the observing condi 2° 50', or 0.84 mm., in diameter. Pre tions was allowed as a precaution. vious determination on W . gave the The limitation of the exposure to following data: rod-free area, hori 0.1 second precluded eye movements 11 zontal diameter 0.789 mm., vertical which would have had two disturbing diameter, 0.740 mm.; pigmented area, effects: (1) a change in fixation and 0.66 mm. (average) ; nonvascular area, consequently in the location of the horizontal diameter 0.52 mm., vertical image on the area centralis; and (2) an diameter 0.535 mm. Whether the increase in acuity due to movement of • general field tested is concentric with the image 2 . any or all of those mentioned above Experimental procedure: The lines can not, of course, be determined. of the test object were exposed in four The total number of judgments different directions: horizontal, verti given for each area was approximately cal, and right and left oblique. sixty, and the total number for each With a given fixation point, the test eye two thousand. object was set with the lines a given In arriving at the acuity for each distance apart and in a given axis, and area tested, the judgments were scored the pendulum was swung. The sub as follows: each correct "certain" was ject gave his judgment as to the direc counted as two points, each correct tion of the lines, classing it as "certain" "uncertain" as one point, and each "un or "uncertain", or as "unknown". The known" or incorrect judgment as 0. separations and directions of the lines This seemed as simple a method as was were changed in irregular order; but practicable. It is open to the criticism equal numbers at each separation and that if correct guesses count, incorrect direction were given. guesses should discount. As the in After a little experience the critical correct guesses were very few in num range of settings with a given fixation ber and the incorrect certains still point could be forecast rather closely. fewer, their omission did not appre In this range five judgments were ciably affect the result. On this basis recorded for each of the four positions then a score of five in five trials was of the test object at each of the scale considered the fifty per cent mark, or settings used. On an average, three the threshold acuity. This median and settings of the scale included the its probable error were determined by critical range, four out of five correct customary methods. "certains" and four out of five "un For calculation of the size of retinal knowns" being considered satisfactory images and visual angles, the following limits. method was used 26 : An inherent source of variability is Let the difficulty of maintaining accurate x = distance of object from first fixation, particularly with small de focal point, grees of excentricity. Fatigue was y = size of object found to be such an important factor y' = size of retinal image that only short periods of observation wf = angle in radians subtended were employed, with ample rest be by object at first nodal tween. The best proof of the care point and by image at taken on these points is that the varia second nodal point, tions, and consequently the probable and errors, of the results are as small as F = refractive power of eye they are. For each eye the acuity was deter (58.64 D. for Gullstrand's schematic eye). mined for thirty-three retinal areas: for that surrounding the axis of fixa Then tion and for eight tangent areas on i y each side in the horizontal and vertical X X meridians. This covers a field about
951
VISUAL ACUITY and
■('4) approximately
xF In this case, for the test object x = 21 m., while for the screen x = 19.39 m. On this basis the subject's visual angle for the test object and also for the interval between successive fixation points was 10.64', which corresponds to a retinal distance of 0.05277 mm.
The size of retinal image correspond ing to a visual angle of 1' is 4.96 microns. The maximum average axial acuity (determined by fixing the test object) was found to be 1.54 (in the case of W . ) , in which case the distance from the center of the image of a black line to that of the adjacent white line would be 3.22 microns. It is interest ing to compare this figure with that of Fritsch 14 , who gives the average interconal distance as about 3 microns! Results and discussion: Although a greater number of observations would undoubtedly give a more completely representative curve of acuity, the
TABLE 1
Visual acuity and threshold for each part of visual field tested (W). Average for all directions
Direction of lines of test obj ect Excentricity Direct fixation 0' Nasal meridian 10.64' 21.27' 31.91' 42.54' ' 53.18' 63.82' 74.46' 85.08' Temporal meridian 10.64' 21.27' 31.91' 42.54' 53.18' 63.82' 74.46' 85.08' Inferior meridian 10.64' 21.27' 31.91' 42.54' 53.18' 63.82' 74.46' 85.08' Superior meridian 10.64' 21.27' 31.91' 42.54' 53.18' 63.82' 74.46' 85.08'
right oblique acuity
left oblique acuity
vertical acuity
1.53
1.44
1.63
1.56
1.60 1.38 1.28 1.12 1.08 1.01 0.92 0.92
1.30 1.08 1.14 1.05 1.03 0.98 0.92 0.91
1.67 1.38 1.30 1.17 1.17 1.05 0.94 0.92
1.54 1.53 1.42 1.26 1.24 1.17 1.17 1.05
1.40 1.28 1.30 1.17 1.24 0.99 0.99 0.94
1.49 1.35 1.30 1.23 1.21 0.96 0.94 0.99
1.65 1.38 1.42 1.30 1.24 1.07 1.01 0.98
1.37 1.30 1.03 0.89 0.82 0.76 0.71 0.59
1.28 1.08 1.08 0.78 0.82 0.73 0.69 0.64
1.38 1.33 1.05 0.94 0.83 0.83 0.69 0.67
1.47 1.26 1.24 0.97 0.91 0.94 0.75 0.73
horizontal acuity
acuity P.E.
threshold seconds
1.54 ±0.0057
39.0
1.53+0.0063 1.34+0.0101 1.29+0.0073 1.15+0.0050 1.13+0.0057 1.05+0.0050 0.99+0.0066 0.95+0.0049
39.2 44.8 46.5 52.2 53.1 57.1 60.6 63.2
1.49 1.50 1.51 1.37 1.35 1.26 1.19 1.10
1.51 1.38 1.38 1.27 1.26 1.07 1.03 1.00
39.7 43.5 43.5 47.2 47.6 56.1 58.3 60.0
1.56 1.38 1.17 0.99 1.05 0.92 0.75 0.70
1.53 1.19 1.15 0.96 0.87 0.78 0.71 0.70
1.44 1.24 1.11 0.91 0.89 0.80 0.72 0.66
41.7 48.4 54.1 65.9 67.4 75.0 83.3 90.9
1.53 1.53 1.30 1.12 0.96 0.96 0.91 0.73
1.44 1.31 1.28 1.08 0.96 0.94 0.85 0.78
1.46 1.36 1.22 1.03 0.92 0.92 0.80 0.73
41.2 44.1 49.2 58.3 65.2 65.2 75.0 82.2
•
952
FRANK W. WEYMOUTH AND OTHERS TABLE 2
Table giving for all three subjects the average visual acuity and threshold at each distance from the axis of fixation. Excentricity of center of area tested angular distance minutes 0 10.64 21.27 31.91 42.54 53.18 63.82 74.46 85.08
retinal distance mm. 0 0.0528 0.1055 0.1583 0.2111 0.2639 0.3166 0.3694 0.4222
Average of all meridians Wh
W
R
acuity
seconds
acuity
seconds
acuity
seconds
1.54 1.49 1.33 1.25 1.09 1.05 0.96 0.89 0.83
39.0 40.3 45.1 48.0 55.5 57.2 62.5 67.5 72.3
1.45
41.4
0.98
61.2
1.19 1.12 1.02 0.94 0.81 0.78 0.66
50.4 53.6 58.8 63.8 74.1 76.9 90.9
0.77 0.82 0.72 0.73 0.67 0.54 0.51
77.9 73.2 83.3 82.2 89.6 111.1 117.7
present data, which are more extensive and accurate than those previously available, seem to show conclusively several important features. First : The area centralis shows a
uniform sensory gradient essentially similar to that for the entire retina as determined by Wertheim 27 . This is clearly shown in figure 1, and by cornparison of figures 5 and 6.
ANGULAR DISTANCE BETW££N F/XATIOU POINT AND IM/K£
Fig. 1. (Weymouth). Comparison of Wertheim's data on central visual acuity (circles) with those of W. in the present work (points). The boundaries of the nonvascular, pigmented, and rod-free areas of W. are indicated. The ordinates represent the logarithms of the visual acuities scaled to a fixation value of unity for comparison.
VISUAL ACUITY
The peripheral decline of acuity is without apparent breaks or changes, but forms a continuous gradient on which the anatomical margins of the fovea or other central areas are not indicated. In other words, the margins of the rod-free area, of the pigmented area (macula), and of the nonvascular area are not reflected in the acuity, whatever other physiological relations may be shown for them. W e must conclude that, as far as acuity is con cerned, foveal and extrafoveal photopic or light-adapted vision are basically the same. The angular limits of "central acuity" can be set only arbitrarily. Second: The gradient is a continu ous one from a sharp maximum at the axis of fixation (presumably the center of the fovea); and points separated radially by as little as 10.64' or 0.0528 mm. show distinct differences of acuity. The general averages of the three sub jects are shown in figure 2. It must be recalled that successive points of fixation caused images of the test object to fall on the retina in the
U.64-'
21. ZT
31.9/'
953
form of tangent circles of 52.77 microns diameter along the horizontal and vertical meridians. Each determina tion, although plotted as a point, tests, then, the acuity of a circular area of about 0.002187 sq.mm. or 2187 sq. microns, and containing about 227 cones. Whether the acuity represents in each case the average or the maximum sensitivity of the area cannot, of course, be determined. If it is the average, the results tend to be smoothed, a process which would reduce the sharpness of the central peak. If it is the maximum, as seems more probable, then we are testing in each area the portion nearest the axis of fixation, and the first excentric determination is in reality more nearly at 5' from the axis pf fixation than at 10.64' (corresponding to the center of the area). The net effect in such a case is to necessitate plotting each determination approximately 5' nearer the axis of fixation. The relation between the peripheral points or areas is not seri-
4Z.54-'
53./a'
63.az?
74.46'
AUGL£ FROM Axis OF FIXATION
Fig. 2 (Weymouth). The average acuity of the three subjects scaled to a fixation acuity of unity for comparison.
6&06'
954
FRANK W. WEYMOUTH AND OTHERS
ously changed, but the first interval, between fixation and 10.64', is reduced by almost half. As the first peripheral value is plotted at 10.64', the apparent sharpness of the peak in acuity at fixa tion is less than it probably should be. This peak has important bearings on the relation of the sensory gradient to eye movements and fixation, as will be pointed out later.
error of ± 0.0076. Probable errors and their relative magnitude for the nasal meridian of W. are shown on the curve in figure 3. This meridian is entirely characteristic and shows a much natter gradient than either of the two vertical meridians. The most difficult comparison is that of fixation and a point 10.64' excentric.
40"
45-
I
i-60'
/0.64'
2/. 27' -31.91' 4-2.54-' 53.18' ANGLE PROM AXIS OF FIXATIO/V
63.8?
74.46'
85.08'
Fig. 3 (Weymouth). Acuity for the nasal meridian of W.'s visual field with the probable errors of each determination. Successive d e t e r m i n a t i o n s seem in m o s t i n s t a n c e s t o b e significantly different. T h u s p o i n t s a t 53 + ' and 64 + ' on t h e s m o o t h e r of t h e less s h a r p g r a d i e n t s for W . s h o w a difference in visual a c u i t y of 0.08 w i t h a p r o b a b l e
W . w a s t h e only subject w h o felt t h a t h e could satisfactorily m a i n t a i n fixa tion a t t h a t slight excentricity, the a n g u l a r n e a r n e s s of the test object b e i n g too d i s t r a c t i n g for t h e less ex perienced subjects. S u c h a comparison
TABLE 3
Position of test object Nasal Temporal Inferior Superior
Fixation acuity 1.54 1.54 1.S4 1.54
10.64' acuity 1.53 1.51 1.44 1.46
Difference 0.01 0.03 0.10 0.08
P.E. of difference ±0.0084 ±0.0087 ±0.0093 ±0.0089
VISUAL ACUITY
955
r*T
45"
50"
J 70"
-e
21.27'
31.91' ANGLE
-42.54'
FROM
AXIS
53.I&' OF
63.32'
74.46'
<35.0&
FIXATION
Fig. 4 (Weymouth). The acuity of W. in the four meridians of the visual field. SUPERIOR
TEMPORAL
90' ao' 70' 6cr so- *& 30- zo' io-
FROM
IO1
AXIS
zo' 30' -ro' so1 60 ro- ec sor OF
FIXATION
Fig. 5 (Weymouth). Isopteral chart of W. showing points of equal acuity together with the diameters of the nonvascular (N.V.), pigmented (P.), and the rod-free (R.F.) areas,
956
FRANK W. W E Y M O U T H AND O T H E R S
for W., however, shows differences and probable errors as shown in table 3. The first one of these is not sig nificant and the second is on the borderline, but the iast two are definitely significant, and the whole must be considered so, as in no case is the determination at 10.64' greater than at fixation. Even though this first excentric determination was not ob tained for the other subjects, the trend of the gradient would require a similar difference.
retina, but either the average or the maximum of an area. Third: The different meridians used show different rates of change of acuity, as given for W. in figure 4; the horizontal showing in general the higher acuity in all three subjects. These results are more clearly repre sented in the isopteral diagram (figure 5) in which the points of equal acuity on the four chief meridians of the right eye of W. are connected. The observa tions of Wh. present a similar picture. SUPERIOR
TEMPORAL
35°
30° 25° 20° 15° 10° 5° ANGLE
FROM
0° AXIS
5°
10° 15° 20° 25° 30° 35° 4-0°
OF
FIXATION
Fig. 6 (Weymouth). Isopteral chart of entire visual field based on Wertheim's data for the four principal meridians; for comparison with figure 4.
That the difference is even greater than that shown is indicated by a con sideration of two factors: a. Gross inaccuracies of fixation would tend to be toward the test ob ject rather than away, as it is the center of interest. This tends not only to decrease the apparent difference in acuity but also to increase the probable error by spreading the distribution of judgments. b. As discussed above, each de termination tests, not a point on the
An isopteral graph constructed from the data of Wertheim 27 is given for comparison (figure 6). W e obtained the following order of descending acuity: temporal, nasal, superior, inferior. Wertheim's order for the periphery (points excentric 20° or more) is: temporal, nasal, inferior, superior. The visual field, which is actually an isopter (but for light sense rather than for acuity), shows the order: temporal, inferior, nasal, su perior 12 . The fields for colors are
957
VISUAL ACUITY
similar to that for white light. It is to be noted that the inferior meridian, while of least acuity in and near the fovea, shows a relatively lesser rate of fall of acuity than do the other meri dians, which remain in the same rela tion to each other. An unexpected discovery was that of a relation between the visual acuity and the direction of the lines of the test object with reference to the axis of fixation. In each case the acuity was higher when the lines pointed
A, horizontal meridian tested with horizontal lines. B, horizontal meridian tested with vertical lines. C, vertical meridian tested with vertical lines. D, vertical meridian tested with horizontal lines.
The explanation is not perfectly clear. The right eye of the subject whose values are quoted is not astig matic by the ordinary tests. The ex posure was supposedly short enough to preclude fixative eye movements such
ut r3S"
1.6 1.4
\ x
1.0
0
/0.64-'
21.2?'
<3W ANGLE
Fig. 7 (Weymouth). test object for W.
42.54-' FROM AXIS
33.18' OF
63.82'
74.46'
85.08
FIXATION
Relation between the acuity and the direction of the lines of the
toward the axis of fixation than when they were perpendicular to that direc tion. Thus, it was found that in the vertical meridian the acuity was higher for the vertical direction of the lines than for the horizontal, while in the horizontal meridian the acuity was higher for the horizontal than for the vertical lines, the effect being more marked in the latter case. This is shown graphically in figure 7. It will also be noted that with direct fixation vertical lines are better perceived.
as would tend to blur lines which were not parallel to the direction of move ment, but this factor cannot wholly be excluded nor its importance de termined. The explanation may lie in a different configuration of retinal elements in the meridional direction, giving an actual higher acuity when the points distinguished have their separation at right angles to the meridian. Sensory gradient and fixation: The present investigation seems to have its
958
FRANK W. WEYMOUTH AND OTHERS
greatest significance in relation to fixa tion. Those sense organs presenting an extensive sensory field show differ ences of sensitivity in different parts of this field. If such topographical differences are regular and uniform, we may speak of a sensory gradient or gradient of sensitivity. The eye pre sents such a sensory gradient in a more marked degree than any other recep tor ; the present work serves to extend our knowledge of this gradient into the area centralis; and, as we shall show, such a gradient is fundamental for fixa tion and those eye movements which bring it about. In considering the basis of fixation, we must remember that it is a response on the part of the ocular muscles to a stimulus received on the retina, the re sponse being effected through the central nervous system. The accuracy of such a reaction is, of course, depend ent on the least sensitive element in it, just as the strength of a chain is de pendent on its weakest link. And so, if investigation of the relative sensi tivity of the various elements shows some more accurate than the complete act of fixation itself, then we may rule them out as the limiting factors in fix ation, although all the elements are of course necessary to fixation. For our purposes, the reaction of fixation may be divided into the two elements, sensory and motor, the first including the excitation of the retinal receptors and the integration of the nervous impulses so caused into a per ception in the central nervous system, the second including the activation of the ocular muscles. The accuracy of these two inclusive factors has to some extent been measured; that of their subdivisions has not been analyzed. As to the accuracy of the act of fixation itself, the most careful deter mination is that of Marx and Trendelenburg 22 . With graphic methods ac curate to 15 or 20", they observed in maintained fixation oscillating fluctua tions of about 1' on which were super imposed irregular fluctuations of 4 to 5'. These larger movements they in terpret as due to corrective movements
arising when the image departs more than 2.5' from the center of a fixation area. When two points a short dis tance (18' 17") apart were alternately fixed, the errors were not greater than the variations in fixation of a single point. The limit of accuracy of fixa tion as a whole, then, appears to be 2.5'. The limit of accuracy of the motor part is difficult of determination, since it is almost impossible to separate it from some sensory element. One method of approach to the problem would appear to be that of the thresh old for binocular perception of dis tance (parallax and all distinguishing features of object and surroundings be ing eliminated), so that the determin ing factor is the perception of differ ences in convergence. Fulfilling such requirements are the determinations of Bourdon 5 . Using successive ex posures of a stationary object at dif ferent distances, he obtained a thres hold of about 4' at 25m. The deter minations of Wundt 2 9 , which gave a threshold of 1' 24", are open to objec tion on the grounds of method. Such a determination, however, in volves the perception of changes in the relative position of the two bulbs, a perception which is not necessary to fixation, where the accuracy is checked by exteroceptive sensations from the retina rather than by proprioceptive from the motor apparatus of the bulb. The threshold here cited seems more likely that for the perception than for the motion. Chiba 8 , using the records of Marx and Trendelenburg 22 , considers the small oscillations of the eyeball as the smallest muscular movements ( = 1'). He finds the number in a lateral turn of 40° about equal to the number of fibers in the abducens nerve. While capable of other interpretations, such data are at least highly suggestive, and of course the ultimate limit of control would thus be the coming in or falling out of one nerve fiber. This limit may or may not be 1' and also may or may not be under voluntary control. In other words, we have no definite de-
VISUAL ACUITY termination of the accuracy of the motor element. As for the keenness of the sensory part of the reaction, Averill and Weymouth 2 find that the threshold for the perception of displacements in seg ments of a straight line may be as small as 0.04' (0.02 micron on the retina), an angular distance 1/60 that of the accuracy of fixation. The eye can, then, perceive differences sixty times smaller than it can fix separately; so that fineness of fixation cannot be immediately dependent on fineness of perception. To be distinguished from fineness of perception (or visual acuity in the broad sense) is change of fineness of perception (or sensory gradient). The two do not necessarily parallel each other, for a high acuity may be uni form, giving a low gradient, or a low acuity may fall off rapidly, giving a high gradient. We have left to con sider, then, this sensory gradient. The idea that variation of acuity, or sensory gradient, is the basis of fixa tion is not a new one. Javal 19 pro pounded it as long ago as 1896, and Duane 12 (pages 267, 290, 342) reitera ted it in 1924, although realizing the lack of information regarding sensory gradient within the fovea. Marx and Trendelenburg 22 believe their "fixa tion area" is based on differences of acuity within the area centralis, the image being brought back to the area of maximum acuity as soon as it be comes of appreciably less than the maximum distinctness. To the view that a sensory gradient is the basis of fixation strong support is lent by the work of Simon 24 on fixation in scotopic or dark adaptation. H e finds that with the relative depression of central vision in dark adaptation the most sensitive portion of the retina be comes extracentral, and a new axis of fixation as much as 2° from the one used in bright light may be selected. The direction varies with different sub jects, and fixation is less accurate and rapid. Observations of similar new fixation points in strabismus have been recorded, but accurate information is
959
scarce. Simon believes the position of the fixation point in dark adaptation to rest on a balance between falling acuity and rising sensitivity to light as we pass out of the fovea. While the motor element can not at the present time be entirely eliminated as the possible factor determining the accuracy of fixation, the work of Simon seems to show almost conclusively that the point or axis of fixation is deter mined by the sensory gradient, the im age being made to fall on that part of the retina where it is perceived with greatest distinctness. And it seems en tirely logical that if the sensory gradient determines the area on which the image falls when an object is fixed, it must also determine the accuracy with which the image is maintained on that area. In other words, if the sensory gradient determines the axis of fixation it must also determine the accuracy of fixation. That a significant difference in vis ual acuity exists within 2.5' of the axis of fixation is entirely consistent with the present work. While our nearest determination is probably somewhere between 6' and 11', as brought out above, the results are significant enough to admit a threshold as close to the axis of fixation as 2.5'. Further determinations with more refined methods will doubtless estab lish this threshold and more closely approximate the exact gradient and its peak. Summary The present work is an investigation of the visual acuity of a central retinal region (including the fovea) with a radius of 85' or 0.42 mm. from the axis of fixation. The method of observation gives significant results for three obser vers as indicated by the probable er rors. 1. In the light adapted eye a uniform sensory gradient is shown to exist in this central area similar to that found in the entire retina (cf. Wertheim, Aubert, Fick, and others). The visual acuity attains a sharp maximum at the axis of fixation; it decreases rapidly but regularly in all directions; it shows
960
FRANK W. W E Y M O U T H AND O T H E R S
no breaks or marked variations in rate 3. The horizontal and vertical meridof change at the margins of any of the ians (the only ones tested) are shown known anatomical areas (fovea, rod- to have different rates of decrease of free area, pigmented area or macula, visual acuity from the axis of fixation. or nonvascular area). 4> T h e a c u i t y i s s h o w n t o b e h i g h e r 2. A significant difference is shown w n e n the lines of the test object point to exist for two observers between di- toward the axis of fixation. rect fixation and 22' and for one obr^, ,, , , ... c i n, . • ,< . .. , 5. 1 hese results strongly support the server for 11% showing that the grad. ,, , ., A- K ■ »L ient continues to the v i r y center of the ™ w h a t t h e s e n s o r v & r a d ' e n t 1S, * h e retina. A similar retinal gradient is b a s l c f a c t o r l n e v e movements and fixatlon indicated by Wertheim to 2° 30' and by Aubert to 1° 15'. Stanford University. Bibliography 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
Aubert, Hermann. Pfliiger's Arch. f. d. ges. Physiol., 1886, v. 39, pp. 347-370. Averill, H. L., and Weymouth, F. W. Jour. Comp. Psych., 1925, v. 5, pp. 147-176. Behn, U. Ber. d. deutscher physikal. Gesellsch., 1906, v. 4, pp. 205-208. Benedict, F. G., Miles, W. R., Roth, P., and Smith, H. M. Human vitality and effi ciency under prolonged restricted diet. Carnegie Inst. Pub. no. 280, 1919, pp. 169176 and 607-611. Bourdon, B. La perception visuelle d'espace. Paris, 1902, p. 237. Burchardt, M. Internationale Sehproben, 4 ed. Berlin, 1893, p. 11. Cady, Francis E., and Dates, Henry B. Illuminating Engineering. New York, 1925. Chiba, M. Pfliiger's Arch. f. d. ges. Physiol., 1926, v. 212, pp. 150-157. Cobb, Percy W. Jour. Exp. Psychol., 1927, v. 10, pp. 350-364. Cobb, Percy W. Trans. Ilium. Eng. Soc, 1928, v. 23, pp. 496-506. Dodge, Raymond. Psychological Review Monographs, 1907, v. 8, p. 4. Duane, Alexander. Fuchs's Textbook of Ophthalmology, 8th ed. Philadelphia, 1924. Fick, A. Eugen. Arch. f. Ophth., 1898, v. 45, pp. 336-356. Fritsch, Gustav. Uber Bau und Bedeutung der Area centralis des Menschen. Berlin, 1908. Hartridge, H. Jour. Physiol., 1922, v. 57, pp. 52-67. Ives, Herbert E. Electrical World, 1910, v. 40, p. 939. Ives, Herbert E. Abst. Bull. Phys. Lab. Nat. Electr. Lamp Assoc, 1913, v. 1. Ives, Herbert E. Jour. Opt. Soc. Am., 1917, v. 1, pp. 101-107. Javal, Emile. Manuel du Strabisme. Paris, 1896, p. 28. Johnson, H. M. Jour. Animal Behavior, 1914, v. 4, pp. 319-339. Johnson, H. M. Jour. Exp. Psychol., 1924, v. 7, pp. 1-44. Marx, Eugen, and Trendelenburg, Wilhelm. Zeit. f. Psychol. u. Physiol. d. Sinnesorg., sec. 2, 1911, v. 45, pp. 87-102. Miles—see Benedict and Miles. Simon, Richard. Zeit. f. Psychol. u. Physiol. d. Sinnesorg., 1904, sec. 2, v. 36, pp. 186-193. Snell, Albert C, and Sterling, Scott. Arch, of Ophth., 1925, v. 54, pp. 443-461. Southall, James P. C. Mirrors, Prisms, and Lenses. New York, 1923, p. 448. Wertheim, Th. Zeit. f. Psychol. u. Physiol. d. Sinnesorg, 1894, sec. 2, v. 7, pp. 172189. Wood, Casey. Amer. Encycl. of Ophth., 1918, v. 13, p. 10019, and v. 6, p. 4640. Wundt, Wilhelm. Beitrage zur Theorie der Sinneswahrnehmung. Leipzig and Heidel berg, 1862, p. 195.